# sinan

Version 1.1 (172 KB) by
Updated 3 Sep 2023

clear all; clc; close all; clf;
sinan = sinan();
t0 = 0; tfinal = 60; N = 100;
h = (tfinal-t0)/N;
t = t0:h:tfinal;
%% Initial conditions
y0=[100, 10, 20];
y01=[100];
%% Parameters
Lambda = 0.1; beta = 0.4; mu = 0.01; gamma = 0.7; % parameters for model 1
a = 0.2; % parameter for model 2
Models
SIR Epidemic model
subject to
Decay model
subject to
%% Models
model_1 = @(t, X) [Lambda- beta*X(1)*X(2);
beta*X(1)*X(2)-(gamma+mu)*X(2);
mu*X(2)];
model_2 = @(t, y) -a*y;
% fractional order
alpha = 1;
% Choose a solver
solver_1 = 'caputo';
solver_2 = 'abc';
solver_3 = 'CLASSICAL';
% How to solve a system of equations?
[t_euler_caputo_1, y_euler_caputo_1] = sinan.euler(model_1, alpha, t, h, y0, solver_1);
[t_euler_ABC_1, y_euler_ABC_1] = sinan.euler(model_1, alpha, t, h, y0, solver_2);
[t_euler_clas_1, y_euler_clas_1] = sinan.euler(model_1, alpha, t, h, y0, solver_3);
[t_rk4_caputo_1, y_rk4_caputo_1] = sinan.rk4(model_1, alpha, t, h, y0, solver_1);
[t_rk4_ABC_1, y_rk4_ABC_1] = sinan.rk4(model_1, alpha, t, h, y0, solver_2);
[t_rk4_clas_1, y_rk4_clas_1] = sinan.rk4(model_1, alpha, t, h, y0, solver_3);
% How to solve an equation?
[t_euler_caputo_2, y_euler_caputo_2] = sinan.euler(model_2, alpha, t, h, y01, solver_1);
[t_euler_ABC_2, y_euler_ABC_2] = sinan.euler(model_2, alpha, t, h, y01, solver_2);
[t_euler_clas_2, y_euler_clas_2] = sinan.euler(model_2, alpha, t, h, y01, solver_3);
[t_rk4_caputo_2, y_rk4_caputo_2] = sinan.rk4(model_2, alpha, t, h, y01, solver_1);
[t_rk4_ABC_2, y_rk4_ABC_2] = sinan.rk4(model_2, alpha, t, h, y01, solver_2);
[t_rk4_clas_2, y_rk4_clas_2] = sinan.rk4(model_2, alpha, t, h, y01, solver_3);
figure(1)
plot(t_euler_caputo_1, y_euler_caputo_1(:, 1), 'r', t_euler_ABC_1, y_euler_ABC_1(:, 1), 'b', t_euler_clas_1, y_euler_clas_1(:, 1), 'k')
legend('Euler caputo', 'Euler abc', 'Euler classical')
figure(2)
plot(t_rk4_caputo_1, y_rk4_caputo_1, 'r', t_rk4_ABC_1, y_rk4_ABC_1, 'b', t_rk4_clas_1, y_rk4_clas_1, 'k')
legend('rk4 caputo', 'rk4 abc', 'rk4 classical')
figure(3)
plot(t_euler_clas_1, y_euler_clas_1, 'r', t_rk4_clas_1, y_rk4_clas_1, 'b')
legend('euler classical', 'rk4 classical')
figure(4)
plot(t_euler_caputo_2, y_euler_caputo_2, 'r', t_euler_ABC_2, y_euler_ABC_2, 'b', t_euler_clas_2, y_euler_clas_2, 'k')
legend('Euler caputo', 'Euler abc', 'Euler classical')
xlabel('time (t)')
ylabel('y(t)')
figure(5)
plot(t_rk4_caputo_2, y_rk4_caputo_2, 'r', t_rk4_ABC_2, y_rk4_ABC_2, 'b', t_rk4_clas_2, y_rk4_clas_2, 'k')
legend('rk4 caputo', 'rk4 abc', 'rk4 classical')
xlabel('time (t)')
ylabel('y(t)')
figure(6)
plot(t_euler_clas_2, y_euler_clas_2, 'r', t_rk4_clas_2, y_rk4_clas_2, 'b')
legend('euler classical', 'rk4 classical')
xlabel('time (t)')
ylabel('y(t)')

### Cite As

Muhammad Sinan (2024). sinan (https://www.mathworks.com/matlabcentral/fileexchange/132812-sinan), MATLAB Central File Exchange. Retrieved .

Sinan, Muhammad. Sinan. Zenodo, 2023, doi:10.5281/ZENODO.8189815.

View more styles
##### MATLAB Release Compatibility
Created with R2022b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes
1.1

The howTO file with some changes and the figures generated and the howTO file are added. You can check the default results for your guidance.

1.0